Need help with this problem

2. (30 pts) In the town of Riskville, there are 3 kinds of people: Type A. Type B. and Type C. They all have different probabilities of having an accident next year that will cost $10,000 in medical bills. Type A people have a 10% probability. Type B people have a 40% probability. Type C people have an 80% probability. There are 100 Type A people. 30 Type B people, and 10 Type C people. A new insurance firm shows up in town, CoverCo. that knows the share of the population that are Type A, B. and C citizens, but can't tell who is who for any given individual. Everyone knows their own expected accident probabilities. (a) (8 pts) What are the expected medical costs of a Type A person? Type B? Type C? (b) (8 pts) Show that, if CoverCo charges a premium designed such that they exactly cover their expected costs if everyone buys insurance, they'll charge $2.143 a year (rounded, to the nearest dollar). Hint: don't forget how many of each type there are! (c) (7 pts) Assume all the residents of Riskville are risk neutral (e.g., they will buy actuarially fair insurance if offered, but won't pay a risk premium). If CoverCo charges $2.143 a year for insurance, how much money will CoverCo lose next year? You can round to the nearest thousand dollars if you're worried about precision. (d) (7 pts) What kind of market failure is causing this problem? Assume the firm adjusts its prices each year, always aiming to break even. What will the eventual market price of insurance be